Making a betting gui help?

The problem wasn't only the part about the math.random. There were also small mistakes.

The problem about the math.random was that you need to find a way to get a random player using math.random. Like how Cawlonee said, go to this site: math.random(). #game.Players:GetChildren() returns the amount of players in-game. It's the same as game.Players.NumPlayers. When math.random() is left blank, it returns a "1" or a "0". Anyway, after it chooses a random number, It chooses a random player. If it returns a 10, it would take the 10th player in alphabetical order.

Another problem was the for loop. If you look on the wiki page here, you can see there is no, if i == 0 then. They end with the keyword end. You see, if for loops have 3 different numbers, the loop keeps looping until the i is equal to the 2nd number in the chain of those 3 numbers.

The last problem was that I forgot to delete the "ends" at the end. So if there is red lines under the "ends".

Also, There is one more error with your script near the for loop part.

I also added the, "if winner.ClassName == "Player" then" to check if the "winner" or "chosen player" is an actual player.

while wait(600) do -- wait 10 minutes before it appears again
local checker = Instance.new("StringValue")
    script.Parent.Frame.Visible = true
    for i, v in pairs(game.Players:GetPlayers()) do -- gets all players
        local button = Instance.new("TextButton", script.Parent.Frame)
        button.Text = v.Name
        button.BackgroundTransparency = 0.75
        button.BackgroundColor3 = Color3.new(Vector3.new(0,0,0))
        local betsLabel = Instance.new("TextLabel", button)
        local bets = Instance.new("IntValue", betsLabel)
        betsLabel.Text = bets.Value
        betsLabel.BackgroundTransparency = 1
        betsLabel.TextColor3 = Color3.new(Vector3.new(255,255,255))
        v.MouseButton1Click:connect(function()
            bets.Value = bets.Value + 1
checker.Name = [[I don't know how you would do this, but if someone clicks on the person to bet on them, make the checker name be that persons name.]] --EDIT THIS PART.
checker.Parent = v
        end)
        for i = 30, 0, -1 do -- timer
            local timeL = Instance.new("TextLabel", script.Parent.Frame)
            timeL.Text = "Time Left: ".. i
wait(1) --Add this so the timer doesn't go down immediately.
local winner = game.Players:GetChildren()[math.random(1,#game.Players:GetChildren())]
if winner.ClassName == "Player" then
local checkforchecker = game.Players:GetChildren()
for i = 1, #checkforchecker do
if checkforchecker[i].ClassName == "Player" then
local bet = checkforchecker[i]:GetChildren()
for i = 1, #bet do
if bet[i]:IsA("Instance") then
if bet[i].Name = winner.Name then
bet[i].Parent.Win.Value = bet[i].Parent.Win.Value --EDIT THIS PART
end
end
end
--Rest of the script.
end
            end
        end
    end
end

I'm not sure exactly what you wanted, but I'll happily explain how math.random works.

Wiki Page

local number = math.random(MinNumber,MaxNumer)

It takes two numbers and returns a random integer between them, like so.

print(math.random(1,10)) -- 10
print(math.random(1,10)) -- 2
print(math.random(1,10))  -- 7

You can get a random player like this:

randomPlayer = game.Players:GetChildren()[math.random(1,#game.Players:GetChildren())]

It's creating a table of random players, and indexing it with a random number between 1 and the total number of players.